ONT Re: Inquiry Into Inquiry
¤~~~~~~~~~¤~~~~~~~~~¤~ANAMNESIS~¤~~~~~~~~~¤~~~~~~~~~¤
| It may be added that algebra was formerly called 'Cossic', in English, or the 'Rule of Cos';
| and the first algebra published in England was called "The Whetstone of Wit", because the
| author supposed that the word 'cos' was the Latin word so spelled, which means a whetstone.
| But in fact, 'cos' was derived from the Italian, 'cosa', thing, the thing you want to find,
| the unknown quantity whose value is sought. It is the Latin 'caussa', a thing aimed at,
| a cause. (CSP, NEM 2, 50).
|
| Charles Sanders Peirce, 'The New Elements of Mathematics',
| Carolyn Eisele (ed.), Mouton, The Hague, Netherlands, 1976.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| At the end of my last lecture I had just enunciated three propositions
| which seem to me to give to pragmatism its peculiar character. In order
| to be able to refer to them briefly this evening, I will call them for the
| nonce my cotary propositions. 'Cos', 'cotis', is a whetstone. They appear
| to me to put the edge on the maxim of pragmatism. (LOP 1903, 241; CP 5.180).
|
| These 'cotary' propositions are as follows:
|
| 1st, 'Nihil est in intellectu quin prius fuerat in sensu'
| [nothing exists in intellect that is not first in senses].
| I take this in a sense somewhat different from that which
| Aristotle intended. By 'intellectus' I understand the 'meaning'
| of any representation in any kind of cognition, virtual, symbolic,
| or whatever it may be. Berkeley and nominalists of his stripe deny
| that we have any idea at all of a triangle in general, which is neither
| equilateral, isosceles, nor scalene. But he cannot deny that there are
| propositions about triangles in general which propostions are either true
| or false; and as long as that is the case, whether we have an 'idea' of a
| triangle in some psychological sense or not, I do not, as a logician, care.
| We have an 'intellectus', a meaning, of which the triangle in general is an
| element. As for the other term, 'in sensu', that I take in the sense of in
| a 'perceptual judgment', the starting point or first premiss of all critical
| and controlled thinking. I will state presently what I conceive to be the
| evidence of the truth of this first cotary proposition. But I prefer to
| begin by recalling to you what all three of them are.
|
| The second is that perceptual judgments contain general elements, so that universal
| propositions are deducible from them in the manner in which the logic of relations
| shows that particular propositions usually, not to say invariably, allow universal
| propositions to be necessarily inferred from them. This I sufficiently argued in
| my last lecture. This evening I shall take the truth of it for granted.
|
| The third cotary proposition is that abductive inference shades into perceptual judgment
| without any sharp line of demarcation between them; or in other words our first premisses,
| the perceptual judgments, are to be regarded as an extreme case of abductive inferences, from
| which they differ in being absolutely beyond criticism. The abductive suggestion comes to us
| like a flash. It is an act of 'insight', although of extremely fallible insight. It is true
| that the different elements of the hypothesis were in our minds before; but it is the idea
| of putting together what we had never before dreamed of putting together which flashes the
| new suggestion before our contemplation.
|
| On its side, the perceptive judgment is the result of a process, although of a process
| not sufficiently conscious to be controlled, or to state it more truly not controllable
| and therefore not fully conscious. If we were to subject this subconscious process
| to logical analysis we should find that it terminated in what that analysis would
| represent as an abductive inference resting on the result of a similar process
| which a similar logical analysis would represent to be terminated by a similar
| abductive inference, and so on 'ad infinitum'. This analysis would be precisely
| analogous to that which the sophism of Achilles and the tortoise applies to the chase
| of the tortoise by Achilles, and it would fail to represent the real process for the same
| reason. Namely just as Achilles does not have to make the series of distinct endeavors which
| he is represented as making, so this process of forming the perceptual judgment because it is
| subconscious and so not amenable to logical criticism does not have to make separate acts of
| inference but performs its act in one continuous process. (LOP 1903, 241-242; CP 5.181).
|
| It appears to me, then, that my three cotary propositions are satisfactorily grounded.
| Nevertheless, since others may not regard them as so certain as I myself do, I propose
| in the first instance to disregard them, and to show that, even if they are put aside as
| doubtful, a maxim practically little differing in most of its applications from that of
| pragmatism ought to be acknowledged and followed; and after this has been done, I will
| show how the recognition of the cotary propositions will affect the matter.
|
| I have argued in several of my early papers that there are but three essentially
| different modes of reasoning: Deduction, Induction, and Abduction. I may mention
| in particular papers in the 'Proceedings of the American Academy of Arts and Sciences'
| for April & May 1867. I must say, however, that it would be very easy to misunderstand
| those arguments. I did not at first fully comprehend them myself. I cannot restate the
| matter tonight, although I am very desirous of doing so, for I could now put it in a much
| clearer light. I have already explained to you briefly what these three modes of inference,
| Deduction, Induction, and Abduction are. I ought to say that when I described induction
| as the experimental testing of a hypothesis, I was not thinking of experimentation in
| the narrow sense in which it is confined to cases in which we ourselves deliberately
| create the peculiar conditions under which we desire to study a phenomenon. I mean
| to extend it to every case in which, having ascertained by deduction that a theory
| would lead us to anticipate under certain circumstances phenomena contrary to what
| we should expect if the theory were 'not' true, we examine the cases of that sort
| to see how far those predictions are borne out. (LOP 1903, 248-249; CP 5.195).
|
| If you carefully consider the question of pragmatism you will see
| that it is nothing else than the question of the logic of abduction.
| That is, pragmatism proposes a certain maxim which, if sound, must
| render needless any further rule as to the admissibility of hypotheses
| to rank as hypotheses, that is to say, as explanations of phenomena
| held as hopeful suggestions; and furthermore, this is 'all' that the
| maxim of pragmatism really pretends to do, at least so far as it is
| confined to logic, and is not understood as a proposition in psychology.
| For the maxim of pragmatism is that a conception can have no logical
| effect or import differing from that of a second conception except so
| far as, taken in connection with other conceptions and intentions, it
| might conceivably modify our practical conduct differently from that
| second conception. Now it is indisputable that no rule of abduction
| would be admitted by any philosopher which should prohibit on any
| formalistic grounds any inquiry as to how we ought in consistency
| to shape our practical conduct. Therefore, a maxim which looks only
| to possibly practical considerations will not need any supplement in
| order to exclude any hypotheses as inadmissible. What hypothesis it
| admits all philosophers would agree ought to be admitted. On the
| other hand, if it be true that nothing but such considerations has
| any logical effect or import whatever, it is plain that the maxim
| of pragmatism cannot cut off any kind of hypothesis which ought to
| be admitted. Thus, the maxim of pragmatism, if true, fully 'covers'
| the entire logic of abduction. It remains to inquire whether this
| maxim may not have some 'further' logical effect. If so, it must in
| some way affect inductive or deductive inference. But that pragmatism
| cannot interfere with induction is evident; because induction simply
| teaches us what we have to expect as a result of experimentation, and
| it is plain that any such expectation may conceivably concern practical
| conduct. In a certain sense it must affect deduction. Anything which
| gives a rule to abduction and so puts a limit upon admissible hypotheses
| will cut down 'the premisses' of deduction, and thereby will render a
| 'reductio ad absurdum' and other equivalent forms of deduction possible
| which would not otherwise have been possible. But here three remarks
| may be made. First, to affect the premisses of deduction is not to
| affect the logic of deduction. For in the process of deduction itself
| no conception is introduced to which pragmatism could be supposed to
| object except the act of abstraction. Concerning that I have only time
| to say that pragmatism ought not to object to it. Secondly, no effect
| of pragmatism which 'is consequent upon its effect on abduction' can
| go to show that pragmatism is anything more than a doctrine concerning
| the logic of abduction. Thirdly, if pragmatism is the doctrine that
| every conception is a conception of conceivable practical effects,
| it makes conception reach far beyond the practical. It allows any
| flight of imagination, provided this imagination ultimately alights
| upon a possible practical effect; and thus many hypotheses may seem
| at first glance to be excluded by the pragmatical maxim that are not
| really so excluded. (LOP 1903, 249-250; CP 5.196).
|
| Admitting, then, that the question of Pragmatism is the Question of Abduction,
| let us consider it under that form. What is good abduction? What should an
| explanatory hypothesis be to be worthy to rank as a hypothesis? Of course,
| it must explain the facts. But what other conditions ought it to fulfill
| to be good? The question of the goodness of anything is whether that
| thing fulfills its end. What, then, is the end of an explanatory
| hypothesis? Its end is, through subjection to the test of
| experiment, to lead to the avoidance of all surprise and
| to the establishment of a habit of positive expectation
| that shall not be disappointed. Any hypothesis,
| therefore, may be admissible, in the absence of any
| special reasons to the contrary, provided it be capable
| of experimental verification and only in so far as it is
| capable of such verification. This is approximately the doctrine
| of pragmatism. But just here a broad question opens out before us.
| What are we to understand by experimental verification? The answer to that
| involves the whole logic of induction. Let me point out to you the different
| opinions which we actually find men holding today, perhaps not consistently, but
| thinking that they hold them, upon this subject. (LOP 1903, 250; CP 5.197-198).
|
| Charles Sanders Peirce,
|'Pragmatism as a Principle and Method of Right Thinking',
| The 1903 Harvard 'Lectures on Pragmatism' (= LOP 1903),
| Patricia Ann Turrisi (ed.), SUNY Press, Albany, NY, 1997.
|
| Excerpts from these Lectures constitute CP 5, Bk 1, CP 5.14-212.
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤
| Aristotle's definition of universal predication ['Prior Analytics', 24b, 28-30],
| which is usually designated (like a papal bull or writ of court, from its opening
| words), as the 'Dictum de omni', may be translated as follows: "We call a predication
| (be it affirmative or negative), 'universal', when, and only when, there is nothing among
| the existent individuals to which the subject affirmatively belongs, but to which the
| predicate will not likewise be referred (affirmatively or negatively, according as
| the universal predication is affirmative or negative)." The Greek is: "legomen
| de to kata pantos kategoreisthai otan meden e labein ton tou upokeimenou kath ou
| thateron ou lechthesetai kai to kata medenos osautos" [here, as transliterated].
| The important words "existent individuals" have been introduced into the translation
| (which English idiom would not here permit to be literal); but it is plain that existent
| individuals were what Aristotle meant. The other departures from literalness only serve
| to give modern English forms of expression. Now, it is well known that propositions
| in formal logic go in pairs, the two of one pair being convertible into another by
| the interchange of the ideas of antecedent and consequent, subject and predicate,
| etc. The parallelism extends so far that it is often assumed to be perfect;
| but it is not quite so. The proper mate of this sort to the 'Dictum de omni'
| is the following definition of affirmative predication: We call a predication
| 'affirmative' (be it universal or particular) when, and only when, there is nothing
| among the sensational effects that belong universally to the predicate which will not
| be (universally or particularly, according as the affirmative predication is universal
| or particular), said to belong to the subject. Now, this is substantially the essential
| proposition of pragmaticism. Of course, its parallelism to the 'Dictum de omni' will
| only be admitted by a person who admits the truth of pragmaticism. (CP 5.435).
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.435
¤~~~~~~~~~¤~~~~~~~~~¤~SISENMANA~¤~~~~~~~~~¤~~~~~~~~~¤
HP: We have our threads tangled.
I'm back on "Inquiry Into Inquiry."
Let's focus on the horizontal arrow problem.
HP: Pick up at 08:48 PM 8/13/01 -0400:
http://suo.ieee.org/ontology/msg03111.html
JA: Short answer. Let's think of the horizontal arrows as analogous to perception.
Yes, the "Darts Of Perception".
HP: I would mean by this arrow an epistemic process of
detection, pattern recognition, perception, observation,
measurement (listed roughly in an evolutionary progression).
Most generally, I would call these edges the organism's
construction of an image, using these words in a broad,
partly metaphorical sense.
JA: Okay, so far, so good. But remind me sometime to read you the Peircean revival
of an ancient problem about the relationship of "sensibles" and "intelligibles".
The gist of his solution is that a process very akin to abduction is present in
the most elementary of sensations and perceptions.
HP: Read it to me now. To me this problem -- perception or more generally, pattern recognition --
is the most important stage of inquiry. From what I have read secondhand, I think Peirce
abducted (with little data) a good hypothesis about perception that is consistent with
experiments on real brains, and is now commonly applied in AI, but I would like to
see his words.
JA: Said & Done.
HP: This fundamental pattern recognition problem is neatly evaded in Hertz's first four words:
"We form for ourselves images ..." It's what physicists also evade by names, such as
"epistemic cut", or "observation", or "measurement", where the observer actually
meets the observed, or where all inquiry must begin. I argue that life (and
evolution by natural selection) began with such a distinction between
an active "interpreting" agent and the passive "uninterpreting"
physical world. The recognition of this cut is required for
describing detection. pattern recognition, perception,
observation, measurement, even counting, but why we
place the cut where we do, and what is really
going on is seldom mentioned. But, I think
experiments in cognitive science and AI
have given us some clues.
HP: I will explain later why I think analytic categories of deduction, induction, and abduction
are not adequate for explaining how the brain "forms for itself images." But first, tell me
a little about "sensibles" and "intelligibles."
HP: Last strand:
http://suo.ieee.org/ontology/msg03113.html
HP: Creating machine tools to support the intellect is an aim worthy of discussion.
JA: I am pretty much content to leave the creative stuff to people for a while,
since I have no clue how to automate it, and even if I did I would have to
ask whether it's creative stuff we like or creative stuff we dislike doing.
HP: Don't quit on artificial creativity (AC) just yet.
I agree that brains will out-create computers for
most interesting problems. But there are so many
types of problems. Also, computer models (simulations,
analogs, metaphors) may be instructive or even necessary
to understand brains. My original skepticism has subsided
because of the shift from logic-based, rule-based, or "hard"
computing toward "softer" biological analogs, artificial
neural nets, genetic algorithms, fuzzy logics, and
immersion in rich interactive environments.
My aim may be distinct,
beyond the achievement
in forming performance,
understood information
explaining performance.
Jon Awbrey
¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤~~~~~~~~~¤